Extremal metrics on Hartogs domains

Abstract

An $n$-dimensional Hartogs domain $D_F$ with strongly pseudoconvex boundary can be equipped with a natural \K metric $g_F$. In this paper we prove that if $g_F$ is an extremal \K metric then $(D_F,g_F)$ is biholomorphically isometric to the $n$-dimensional complex hyperbolic space.

14 pages

Cited by in corpus (2)

• Riemannian geometry of Hartogs domains
• Symplectic duality between complex domains